Energy-guided Recursive Model
cs.LG, stat.ML
Submitted: 2026-07-11
Updated: 2026-09-23
Code: https://github.com/yilundu/irem_code_release
License: http://creativecommons.org/licenses/by/4.0/
The gist: Recursive reasoning models address structured problems by repeatedly updating latent states of small neural networks.
Terminology
Abstract
Recursive reasoning models address structured problems by repeatedly updating latent states of small neural networks. However, their test-time scaling lacks a principled inference mechanism: increasing depth or stochastic breadth generates more trajectories without a clear criterion for selection, and existing methods predominantly rely on additional q-heads or heuristic voting. Here, we develop the Energy-guided Recursive Model (ERM), which introduces an intrinsic selection principle based on explicit Hopfield energies. ERM leverages Hopfield-type memories of valid local or global structures to define the selector over candidate trajectories. The resulting energy seamlessly integrates with energy-based techniques such as parallel tempering to enhance sampling efficiency and ranking. With D=64 recurrent steps and K=128 candidates, ERM reaches optimal solutions on Sudoku (98.97%), Pencil Puzzle Bench (PPBench, 88.04%) and Maze (99.30%), improving upon recent Probabilistic Tiny Recursive Model and Equilibrium Reasoners. These results suggest that incorporating explicit energy functions into recursive reasoning offers a principled path toward more effective inference.
Sources
- Probabilistic Tiny Recursive Model
- Training Verifiers to Solve Math Word Problems
- Neural GPUs Learn Algorithms
- Adaptive Computation Time for Recurrent Neural Networks
- Scaling Latent Reasoning via Looped Language Models
- Hierarchical Reasoning Model
- Less is More: Recursive Reasoning with Tiny Networks
- Are Your Reasoning Models Reasoning or Guessing? A Mechanistic Analysis of Hierarchical Reasoning Models
- Pencil Puzzle Bench: A Benchmark for Multi-Step Verifiable Reasoning
- Solve the Loop: Attractor Models for Language and Reasoning
- Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers
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